539.36 Modeling microstructural model of the plasticity deformation theory for quasi-isotropic composite materials

Dimitrienko Y. I. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University), Dimitrienko A. Y. (Lomonosov Moscow State University), Yurin Y. V. (Bauman Moscow State Technical University)

COMPOSITES, NUMERICAL SIMULATION, DEFORMATION THEORY OF PLASTICITY, QUASI-ISOTROPIC MATERIALS, MICROSTRUCTURAL MODEL, ASYMPTOTIC AVERAGING METHOD, FINITE ELEMENT METHOD, DISPERSED-REINFORCED COMPOSITES, METAL COMPOSITES, DEFORMATION DIAGRAMS, INVARIANTS


doi: 10.18698/2309-3684-2021-4-1744


A model of constitutive relations for elastic-plastic composites with cubic symmetry of properties is proposed. This class includes a significant number of composite materials: dispersed-reinforced composites, which have an ordered rather than a chaotic reinforcement system, as well as some types of spatially reinforced composites. To build a model of nonlinear constitutive relations, a tensor-symmetry approach was used, based on the spectral expansions of stress and strain tensors, as well as the spectral representation of nonlinear tensor relations between these tensors. The deformation theory of plasticity is considered, for which the tensor-symmetric approach is used, and specific models are proposed for plasticity functions that depend on the spectral invariants of the strain tensor. To determine the model constants, a method is proposed in which these constants are calculated based on the approximation of deformation curves obtained by direct numerical solution of three-dimensional problems on the periodicity cell of elastic-plastic composites. These problems arise in the method of asymptotic averaging of periodic media. To solve problems on a periodicity cell, a finite element method and special software was used that implements solutions to problems on periodicity cells, developed at the Scientific and Educational Center for Supercomputer Engineering Modeling and Development of Software Packages of Bauman Moscow State Technical University. An example of calculating the constants of a composite model using the proposed method for a dispersed-reinforced composite based on a metal matrix is considered. Also, the verification of the proposed model for various ways of multiaxial loading of the composite was carried out with direct numerical simulation. It is shown that the proposed microstructural model and the algorithm for determining its constants provide a sufficiently high accuracy in predicting the elastic-plastic deformation of the composite.


Mileiko S.T. Oxide-fibre/Ni-based matrix composites – III: A creep model and analysis of experimental data. Composites Science and Technology, 2002, vol. 62, iss. 2, pp.195–204.
Rawal S. Metal-matrix composites for space applications. JOM, 2001, vol. 5, iss. 4, pp. 14–17.
Dvorak G.J. Inelastic deformation of composite materials. Springer-Verlag. 1990, 779 p.
Kovtunov A.I., Mamin S.V., Semistenova T.V. Sloistyye kompozitsionnyye materialy: elektronnoye uchebnoye posobiye. [Layered composite materials: electronic textbook]. Togliatti, TSU Publ., 2017, 75 p.
Nikitin V.S., Polovinkin V.N. Primenenie kompozitnyh materialov v zarubezhnom podvodnom korablestroenii [Application of composite materials in foreign underwater shipbuilding[. Information Agency "PRoAtom" [Electronic resource]. URL: http://www.proatom.ru / (accessed 20.10.2021).
Katsiropoulos Ch.V., Pantelakis Sp.G., Meyer B.C. Mechanical behavior of non-crimp fabric PEEK/C thermoplastic composites. Theoretical and Applied Fracture Mechanics, vol. 52, iss. 2, pp. 122–129.
Adams D.F. Uprugoplasticheskoe povedenie kompozitov. Kompozitsionnye materialy. T. 2: Mekhanika kompozitsionnykh materialov [Elastic-plastic behavior of composites. Composite materials. Vol. 2: Mechanics of composite materials]. Moscow, Mir Publ., 1978, pp. 196–241.
Bilim A.V., Saraev L.A., Sahabiev V.A.The persicularities of two–component composite materials elastic–plastic deformation. Vestnik of Samara University, 1998, no. 4, pp. 113–119.
Nguyen B.N., Bapanapalli S.K., Kunc V., Phelps J.H., Tucker C.L. Prediction of the elastic–plastic stress/strain response for injection–molded long–fiber thermoplastics. Journal of Composite Materials, 2009, vol. 43, no. 3, pp. 217–246.
Pobedrya B.E. Mekhanika kompozitsionnykh materialov [Mechanics of composite materials]. Moscow, Lomonosov Moscow State University Publ., 1984, 324 p.
Vildeman V.E., Sokolkin Yu.V., Tashkinov A.A. Mekhanika neuprugogo deformirovaniya i razrusheniya kompozitsionnykh materialov [Mechanics of inelastic deformation and destruction of composite materials]. Moscow, Nauka Publ., 1997, 288 p.
Manevich L.I., Andrianov I.V., Oshmyan V.G. Mechanics of Periodically Heterogeneous Structures. Springer-Verlag, 2002, 276 p.
Khdir Y.K., Kanit T., Zaïri F., Naït–Abdelaziz M. Computational homogenization of elastic-plastic composites. International Journal of Solids and Structures, 2013, vol. 50, no. 18, pp. 2829–2835.
Dimitrienko Yu.I., Kashkarov A.I., Makashov A.A. Finite element calculation of effective elastic-plastic characteristics of composites based on the method of asymptotic averaging. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2007, no. 1, pp. 102–116.
Dimitrienko Y.I., Sborschikov S.V, Yurin Y.V. Modeling of effective elastic–plastic properties of composites under cyclic loading. Маthematical Modeling and Coтputational Methods, 2020, № 4, pp. 3–26.
Dimitrienko Yu.I., Sborschikov S.V., Prozorovsky A.A., Gubareva E.A., Yakovlev N.O., Erasov V.S., Krylov V.D., Grigorev M.M., Fedonyuk N.N. Development of a multilayer polymer composite material with discrete structural-orthotropic fillers. Composites and Nanostructures, 2014, vol. 6, no. 1, pp. 32–48.
Dimitrienko Y.I., Gubareva E.A., Sborschikov S.V., Bazyleva O.A., Lutsenko A.N., Oreshko E.I. Modeling the elastic–plastic characteristics of monocrystalline intermetallic alloys based on microstructural numerical analysis. Маthematical Modeling and Coтputational Methods, 2015, no. 2, pp. 3–22.
Dimitrienko Y.I., Gubareva E.A., Sborschikov S.V. Multiscale modeling of elastic–plastic composites with an allowance for fault probability. Маthematical Modeling and Coтputational Methods, 2016, № 2, pp. 3–23.
Bensoussan A., Lions J.L., Papanicolaou G. Asympotic analysis for periodic structures. North-Holland, 1978, 721 p.
Bakhvalov N.S., Panasenko G.P. Osrednenie protsessov v periodicheskikh sredakh. Matematicheskie zadachi mekhaniki kompozitsionnykh materialov [Averaging processes in periodic media. Mathematical problems of the composite material mechanics]. Moscow, Nauka Publ., 1984, 352 p.
Sanches–Palensiya E. Neodnorodnye sredy i teoriya kolebaniy [Nonhomoge-neous media and vibration theory]. Moscow, Mir Publ., 1984, 472 p.
Ilyushin A.A. Plastichnost'. Uprugo-plasticheskie deformacii [Plasticity. Elastic-plastic deformations]. Moscow, URSS, 2018, 392 p.
Ilyushin A.A., Lensky V.V. Soprotivlenie materialov [Resistance of materials]. Moscow, Fizmatlit Publ., 1959, 372 p.
Moskvitin V.V. Ciklicheskie nagruzheniya elementov konstrukcij [Cyclic loading of structural elements]. Moscow, URSS, 2019, 344 p.
Bondar V.S., Danshin V.V. Plastichnost'. Proporcional'nye i nepro-porcional'nye nagruzheniya [Plasticity. Proportional and disproportionate loads]. Moscow, Fizmatlit Publ., 2008, 176 p.
Gorshkov A.G., Starovoitov E.I., Yarovaya A.V. Mekhanika sloistyh vyazkoupru-goplasticheskih elementov konstrukcij [Mechanics of layered viscoelastic structural elements]. Moscow, Fizmatlit Publ., 2005, 576 p.
Hill R. Matematicheskaya teoriya plastichnosti [Mathematical theory of plasticity]. Moscow, Gostekhizdat Publ., 1956, 407 p.
Ishlinskiy A.Yu. Prikladnye zadachi mekhaniki. Kniga 1. Mekhanika vyazkoplasticheskih i ne vpolne uprugih tel [Applied problems of mechanics. Book 1. Mechanics of viscoplastic and not completely elastic bodies]. Moscow, URSS, 2021, 358 p.
Dimitrienko Yu.I. Mekhanika sploshnoy sredy. Tom 4. Osnovy mekhaniki tverdogo tela [Continuum Mechanics. Vol. 4. Fundamentals of solid mechanics]. Moscow, BMSTU Publ., 2013, 624 p.
Dimitrienko Yu.I. Tenzornoe ischislenie [Tensor calculus]. Moscow, Higher School Publ., 2001, 576 p.
Dimitrienko Yu.I. Mekhanika sploshnoj sredy. T. 1. Tenzornyj analiz [Continuum Mechanics. Vol. 1. Tensor analysis]. Moscow, BMSTU Publ., 2011, 367 p.
Dimitrienko Y.I., Dimitrienko I.D., Sborschikov S.V. Multiscale hierarchical modeling of fiber reinforced composites by asymptotic homogenization method. Applied Mathematical Sciences, 2015, vol. 9. iss. 145–148, pp. 7211–7220.
Dimitrienko Yu.I., Sborshchikov S.V., Belenovskaya Yu.V., Aniskovich V.A., Perevislov S.N. Modeling microstructural destruction and strength of ceramic сomposites based on the reaction-bonded SiC. Science and Education: Electronic Scientific and Technical Journal, 2013, no. 11, pp. 475–496. DOI: 10.7463/1113.0659438
Dimitrienko Yu.I., Kashkarov A.I., Makashov A.A. Finite element calculation of effective elastic-plastic characteristics of composites based on the method of asymptotic averaging. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2007, no. 1, pp. 102–116.
Certificate no. 2019666176 Programma NonlinearEl_Disp_Manipula dlya prognozirovaniya diagramm nelinejno-uprugogo deformirovaniya dispersno-armirovannyh kompozitov pri malyh deformaciyah na osnove konechno-elementnogo resheniya 3D lokal'nyh zadach mikromekhaniki: svidetel'stvo ob ofic. registracii programmy dlya EVM [The program NonlinearEl_Disp_Manipula for predicting diagrams of nonlinear elastic deformation of dispersed-reinforced composites under small deformations based on the finite element solution of 3D local problems of micromechanics: certificate of ofic. registration of a computer program] / Yu.I. Dimitrienko, Yu.V. Yurin, S.V. Sobshchikov, I.O. Bogdanov; applicant and copyright holder: BMSTU — no. 2019665098; application 26.11.2019; registered in the register of computer programs 05.12.2019 — [1].
Certificate no. 2019666172 Programma StrengthCom SMCM dlya konechno-elementnogo rascheta prochnostnyh harakteristik kompozitnyh materialov so slozhnoj strukturoj s uchetom nakopleniya mikro-povrezhdenij i kinetiki mezoskopicheskih defektov: svidetel'stvo ob ofic. registracii program-my dlya EVM [The StrengthCom SMCM program for finite element calculation of strength characteristics of composite materials with a complex structure, taking into account the accumulation of micro-damage and the kinetics of mesoscopic defects]: certificate of ofic. registration of a computer program / Yu. I. Dimitrienko, E. A. Gubareva, Yu. V. Yurin, S. V. Sobshchikov, I. O. Bogdanov; applicant and copyright holder: BMSTU — no. 2019665109; application 26.11.2019; registered in the register of computer programs 05.12.2019 — [1].
Certificate no. 2018614767 Programma MultiScale_SMCM dlya mnogomasshtabnogo modelirovaniya napryazhenno-deformirovannogo sostoyaniya konstrukcij iz kompozicionnyh materialov, na osnove metoda mnogourovnevoj asimptoticheskoj gomogenizacii i konechno-elementnogo resheniya trekhmernyh zadach teorii uprugosti [MultiScale_SMCM program for multiscale modeling of the stress-strain state of structures made of composite materials, based on the method of multilevel asymptotic homogenization and finite element solution of three-dimensional problems of elasticity theory]: certificate of ofic. registration of computer programs/ Yu.I. Dimitrienko, S.V. Sborshchikov, Yu.V. Yurin; applicant and copyright holder: BMSTU — no. 2018677684; application 21.02.2018; registered in the register of computer programs 17.04.2018 — [1].


Димитриенко Ю.И., Сборщиков С.В., Димитриенко А.Ю., Юрин Ю.В. Микроструктурная модель деформационной теории пластичности квази-изотропных композиционных материалов. Математическое моделирование и численные методы, 2021, № 4, с. 17–44.



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